Synching iPad With iTunes Apparent Problem

Question

Lately every time I use iTunes on my laptop to synch my apps with my iPad iTunes says that there is less apps on my iPad than there really is. Also it shows that my iPad has more space available than it says I have in settings under "usage" on the iPad. If I choose to remove the apps on the iPad through iTunes instead of manually doing so on the iPad iTunes shows less apps on the iPad through the bar that shows the total amount of space on the iPad and space that is used and by what.
I have noticed this going on for months so I am always removing the apps I want to remove from the iPad manually instead of through iTunes. This way I am not losing any apps that I do want on my iPad and my iPad is remaining the way I want it too. Through this method, I am not noticing any changes through iTunes with the bar that depicts the amount of used and unused space on the iPad, even the correct number of apps on the iPad is correct.
(A) Important Information Regarding the iPad, iPod Touch 4th Generation & iTunes:
1. My iPad is an iPad 4th Generation (or iPad with Retina Display)
2. It is running Software Version: iOS 6.1.3
3. I will not update to iOS 7 (iOS 7.0.4) because I totally hate and dislike iOS 7 and everything about it, I prefer iOS 6.1.3 and iOS 6.1.5 that is on my iPod Touch 4th Generation that is also not able to be upgraded to iOS 7 anyways because iOS 7 isn't supported on it so my intentions are to keep my iPod and my iPad running the iOS 6 operating system. (Because of this, it would be wonderful to get rid of the annoying 1 on the "Settings" app icon notifying about the iOS 7 Update that I have already said I don't want.)
4. Regarding updating apps, not wanting iOS 7 and Apple Devices that can't support iOS 7 (such as the iPod Touch 4th Generations) because many of the app updates that were supported on these earlier devices are saying: "Download the last compatible version? The newer version requires iOS 7 or later." This is truly unacceptable behavior for apps because everyone deserves the right to have the current versions of the apps, especially since some of them had to be paid for with valuable hard earned money. Thus all apps should automatically be compatible with all versions of the software the earlier devices are compatible with (meaning that they can't support iOS 7).
I am suggesting this because this could be the possible reason why the apps through iTunes and the iPad are saying there are less than there really is on my iPad.
(B) Regarding iTunes & Synching With The iPad:
1. My iTunes Software Version is the latest, iTunes Version 11.1.3
2. iTunes with the apps I want to remove still on the iPad (6 total to remove) says that I have 94 apps installed with 8.82GB of free space available. The total amount of GB of space used by the installed apps is: 11.03GB.
3. Removing the 6 apps I want to remove on the iPad through iTunes says that I now only have 80 apps on my iPad after removing them through iTunes and now have a total of 16.01GB of free space available. The total amount of GB of space used by the installed apps is: 3.84GB all of a sudden when only 6 apps were removed supposedly.
4. Of course I decided not to allow these changes to take affect on the iPad and intend to remove a total of 6 apps manually, so instead of clicking "Apply" in iTunes I've clicked "Done"  and then when asked: "Would you like to apply these changes?" I clicked "Don't Apply" and manually removed the 6 apps after disconnecting the iPad from my laptop.
(C) After Removing The Apps Manually From The iPad & Re-Synching With iTunes:
1. With the 6 apps manually removed, iTunes now says that I have 88 apps installed on my iPad. (94-6=88)
2. The total amount of free space on my iPad according to iTunes is 8.91GB of free space available. This matches what my iPad says under "Usage" in the General Tab under "Settings".
3. The total amount of GB space being used by all the apps now currently on my iPad are: 10.91GB.
Now as I was saying earlier about iTunes and synching apps with my iPad saying I have more space  and less apps installed than it really does has officially been proven with the three sections (A-C) of information above. Now I like to know why this is accruing and how can it be corrected so both iTunes and the iPad are showing the correct information when synced?
ALSO NOTE: If anyone tries to tell me or suggest I should install iOS 7, don't bother saying it because I will not upgrade to iOS 7 ever because as I've said I don't like it and in my opinion it looks un-appealing and uninteresting and at the same time I want both my iPod Touch 4th Generation and my iPad 4th Generation (iPad with Retina Display) using the same iOS operating system, as in iOS 6.

Answer 1

Hi, Tony.  
Thank you for visiting Apple Support Communities.
Here is an article that you may find helpful when experiencing this issue.  
iTunes: May become unresponsive when connecting iPhone, iPad, or iPod touch
http://support.apple.com/kb/TS3219
Cheers,
Jason H.